{"title":"Nonlinear vibration of simply supported star-shaped auxetic cylindrical shell","authors":"N. Mohandesi, M. Fadaee, M. Talebitooti","doi":"10.1007/s00419-025-02913-5","DOIUrl":null,"url":null,"abstract":"<div><p>The nonlinear dynamic behavior and primary resonance of star-shaped auxetic cylindrical shells for large deformations are considered. First, the extensional and bending stiffness matrices are introduced in a closed-form relation for the star-shaped auxetic pattern. For this end, Castigliano’s theorem as well as the homogenization technique are applied. According to the classical theory of thin shells, including von Karman’s nonlinear terms, the governing equations of a star-shaped auxetic cylindrical shell are extracted. The Runge–Kutta and multiple scale methods are employed to solve the nonlinear equations of motion of the auxetic cylindrical shell for the Navier-type boundary conditions. The accuracy and stability of solutions are examined by the finite element analysis. The effects of geometrical parameters of a star-shaped auxetic cylinder on its linear and nonlinear vibrations are investigated. The presented mathematical procedure for linear and nonlinear vibration behaviors of auxetic structures can be developed for other auxetic patterns, such as honeycomb, chiral and re-entrant ones.</p></div>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":"95 8","pages":""},"PeriodicalIF":2.5000,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archive of Applied Mechanics","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s00419-025-02913-5","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
The nonlinear dynamic behavior and primary resonance of star-shaped auxetic cylindrical shells for large deformations are considered. First, the extensional and bending stiffness matrices are introduced in a closed-form relation for the star-shaped auxetic pattern. For this end, Castigliano’s theorem as well as the homogenization technique are applied. According to the classical theory of thin shells, including von Karman’s nonlinear terms, the governing equations of a star-shaped auxetic cylindrical shell are extracted. The Runge–Kutta and multiple scale methods are employed to solve the nonlinear equations of motion of the auxetic cylindrical shell for the Navier-type boundary conditions. The accuracy and stability of solutions are examined by the finite element analysis. The effects of geometrical parameters of a star-shaped auxetic cylinder on its linear and nonlinear vibrations are investigated. The presented mathematical procedure for linear and nonlinear vibration behaviors of auxetic structures can be developed for other auxetic patterns, such as honeycomb, chiral and re-entrant ones.
期刊介绍:
Archive of Applied Mechanics serves as a platform to communicate original research of scholarly value in all branches of theoretical and applied mechanics, i.e., in solid and fluid mechanics, dynamics and vibrations. It focuses on continuum mechanics in general, structural mechanics, biomechanics, micro- and nano-mechanics as well as hydrodynamics. In particular, the following topics are emphasised: thermodynamics of materials, material modeling, multi-physics, mechanical properties of materials, homogenisation, phase transitions, fracture and damage mechanics, vibration, wave propagation experimental mechanics as well as machine learning techniques in the context of applied mechanics.